Karhunen Lòeve Transform (KLT)

The KLT is a linear transform where the basis functions are taken from the
statistics of the signal, and can thus be adaptive. It is optimal in the
sense of energy compaction, i.e it places as much energy as possible
in as few coefficients as possible. The KLT is also called Principal
Component Analysis, and for discrete signals, the is also
equivalent with the Singular Value Decomposition.
The transform is generally not separable, and thus the full matrix
multiplication must be performed:

(29)

where the is the basis for the transform. is estimated from a
number of
:

(30)

The adaptiveness is not used in the coder, and the basis functions are
calculated off-line in MatLab.